A small drugstore orders copies of a certain magazine for it magazine rack each week. Let X=demand for the magazine,

Kyran Hudson

Kyran Hudson

Answered question

2021-01-27

A small drugstore orders copies of a certain magazine for it magazine rack each week. Let X=demand for the magazine, with pmf x123456p(x)115215315415515615 Suppose the store owner actually pays $1.00 for each copy of the magazine and the price to customers is $2.00. If magazines left at the end of the week have no salvage value, is it better to order three or four copies of the magazine?

Answer & Explanation

SchulzD

SchulzD

Skilled2021-01-28Added 83 answers

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Jeffrey Jordon

Jeffrey Jordon

Expert2021-10-12Added 2605 answers

3 magazines

For this case the total spent is 2*3 = $ 6

And the net revenue for this case would be:

$4-$6 = -$2 , X=1 (demand 1)

$4*2-$6 = $2 , X=2 (demand 2)

$4*3-$6 = $6 , X=3 (demand 3)

For the values of X=4,5,6 the net revenue will be $6 since the number of magazines is 3

And the expected value for the net revenue would be:

E(R)=115(2)+215(2)+315(6)+415(6)+315(6)+215(6)=7415=4.93

4 magazines

For this case the total spent is 2*4 = $ 8

And the net revenue for this case would be:

$4-$8 = -$4 , X=1 (demand 1)

$4*2-$8 = $0 , X=2 (demand 2)

$4*3-$8 = $4 , X=3 (demand 3)

$4*4-$8 = $8 , X=4 (demand 4)

For the values of X=5,6 the net revenue will be $8 since the number of magazines is 4

And the expected value for the net revenue would be:

E(R)=115(4)+215(0)+315(4)+415(8)+315(8)+215(8)=8015=5.33

As as we can see we have a higher expected value for the case with 4 magazines.

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